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Parisian options with jumps: a maturity–excursion randomization approach

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  • Marc Chesney
  • Nikola Vasiljević

Abstract

This paper introduces an analytically tractable method for the pricing of European and American Parisian options in a flexible jump–diffusion model. Our contribution is threefold. First, using a double Laplace–Carson transform with respect to the option maturity and the Parisian (excursion) time, we obtain closed-form solutions for different types of Parisian contracts. Our approach allows us also to analytically disentangle contributions of the jump and diffusion components for Parisian options in the excursion region. Second, we provide numerical examples and quantify the impact of jumps on the option price and the Greeks. Finally, we study the non-monotonic effects of volatility and jump intensity close to the excursion barrier, which are important for shareholders’ investment policy decisions in a levered firm.

Suggested Citation

  • Marc Chesney & Nikola Vasiljević, 2018. "Parisian options with jumps: a maturity–excursion randomization approach," Quantitative Finance, Taylor & Francis Journals, vol. 18(11), pages 1887-1908, November.
    • Handle: RePEc:taf:quantf:v:18:y:2018:i:11:p:1887-1908
    DOI: 10.1080/14697688.2018.1444785
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    Cited by:

    1. Gongqiu Zhang & Lingfei Li, 2023. "A general approach for Parisian stopping times under Markov processes," Finance and Stochastics, Springer, vol. 27(3), pages 769-829, July.
    2. Gongqiu Zhang & Lingfei Li, 2021. "A General Approach for Parisian Stopping Times under Markov Processes," Papers 2107.06605, arXiv.org.
    3. Yangyang Zhuang & Pan Tang, 2023. "Pricing of American Parisian option as executive option based on the least‐squares Monte Carlo approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(10), pages 1469-1496, October.

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